We develop a two-relaxation-time ($\TRT$) Lattice Boltzmann model
for hydrodynamic equations with variable source terms based on
equivalent equilibrium functions. A special parametrization of the
free relaxation parameter is derived. It controls, in addition to
the non-dimensional hydrodynamic numbers, any $\TRT$ macroscopic
steady solution and governs the spatial discretization of transient
flows. In this framework, the multi-reflection
approach~\cite{MultiRef02,IrDiffPart2} is generalized and extended
for Dirichlet velocity, pressure and mixed (pressure/tangential
velocity) boundary conditions. We propose second and third-order
accurate boundary schemes and adapt them for corners. The boundary
schemes are analyzed for exactness of the parametrization,
uniqueness of their steady solutions, support of staggered
invariants and for the effective accuracy in case of time dependent
boundary conditions and transient flow. When the boundary scheme
obeys the parametrization properly, the derived permeability values
become independent of the selected viscosity for any porous
structure and can be computed efficiently. The linear
interpolations~\cite{BFL2001b,Yu2003} are improved with respect to
this property.